Question

A random sample of 100 employees from 5 different companies was randomly selected, and the number who take public transportation to work was recorded. The results are listed below. Perform a homogeneity of proportions test to test the claim that the proportion who take public transportation to work is the same in all 5 companies. Use α= 0.01.

	1	2	3	4	5
Use Public Trans.	18	25	12	33	22
Don't Use Public Trans.	82	75	88	67	78

a) State the hypothesis and identify which one is the claim. H0 : ________ H1: ________

b) Find the test statistic and corresponding P-value.

c) Make a decision about your hypothesis test. Reject or do not reject the null hypothesis?

d) Interpret your results in terms of the application.

Answer 1

Null hypothesis is that the proportion who take public transportation to work is the same in all 5 companies.

Alternative hypothesis is that the proportion who take public transportation to work is at least different  in one of the 5 companies.

Observed	Expected
18
25
12
33
22
82
75
88
67
78

We can see in the below image that the value in [ ] is ch-square for each cell. After adding them , we have

The chi- square is calculated as

The p-value at 4 degrees of freedom is  .006297. The result is significant at p < .01.

b) As p< 0.01(level of significance), we reject the null hypothesis .

c) We interpret that the proportion who take public transportation to work is at least different  in one of the 5 companies.